San Antonio has a minor league team:
San Antonio Missions: Home
As does San Angelo, about a three hour drive NW of the Alamo City:
San Angelo Colts
As far as eating: La Fogata
La Fogata is one of our favorites for good mexican, and have one, yes just one, of the rita's, I've seen grown men get silly after two. And for BBQ you have to go to Rudy's
Rudy's "Country Store" & Bar-B-Q
Don't forget the swimsuits, head for the Guadalupe river and find a tubing outfitter, spend the day floating down the river.
Another cave in the area that is a lot less commercial, but still very beautiful is "Cave Without a Name" outside of Boerne, well worth the half-hour drive.
cavewithoutaname.com
I also recommend staying off the interstates and sticking to the backroads through the real Texas. Hiway 281 heading north fron San Antonio will take you through some cool little towns all the way to DFW with a short drive east to Waco. While you're in Waco, don't miss the Dr. Pepper Museum and the Texas Rangers (as in the Lone Ranger) Museum. They also have a nice little zoo there.
As everyone else has said, feel free to make contact when you're in the area for further tips and advice.